9×9 Cage Combinations
All valid digit combinations for 9×9 KenKen cages using digits 1–9.
Digits available: 1–9 • Max cage size: 4 cells
+ Addition
2-Cell Cages
| Target | Possible Combinations | Count |
|---|---|---|
| 2+ | 1, 1 | 1 |
| 3+ | 1, 2 | 1 |
| 4+ | 1, 3 2, 2 | 2 |
| 5+ | 1, 4 2, 3 | 2 |
| 6+ | 1, 5 2, 4 3, 3 | 3 |
| 7+ | 1, 6 2, 5 3, 4 | 3 |
| 8+ | 1, 7 2, 6 3, 5 4, 4 | 4 |
| 9+ | 1, 8 2, 7 3, 6 4, 5 | 4 |
| 10+ | 1, 9 2, 8 3, 7 4, 6 5, 5 | 5 |
| 11+ | 2, 9 3, 8 4, 7 5, 6 | 4 |
| 12+ | 3, 9 4, 8 5, 7 6, 6 | 4 |
| 13+ | 4, 9 5, 8 6, 7 | 3 |
| 14+ | 5, 9 6, 8 7, 7 | 3 |
| 15+ | 6, 9 7, 8 | 2 |
| 16+ | 7, 9 8, 8 | 2 |
| 17+ | 8, 9 | 1 |
| 18+ | 9, 9 | 1 |
3-Cell Cages
| Target | Possible Combinations | Count |
|---|---|---|
| 3+ | 1, 1, 1 | 1 |
| 4+ | 1, 1, 2 | 1 |
| 5+ | 1, 1, 3 1, 2, 2 | 2 |
| 6+ | 1, 1, 4 1, 2, 3 2, 2, 2 | 3 |
| 7+ | 1, 1, 5 1, 2, 4 1, 3, 3 2, 2, 3 | 4 |
| 8+ | 1, 1, 6 1, 2, 5 1, 3, 4 2, 2, 4 2, 3, 3 | 5 |
| 9+ | 1, 1, 7 1, 2, 6 1, 3, 5 1, 4, 4 2, 2, 5 2, 3, 4 3, 3, 3 | 7 |
| 10+ | 1, 1, 8 1, 2, 7 1, 3, 6 1, 4, 5 2, 2, 6 2, 3, 5 2, 4, 4 3, 3, 4 | 8 |
| 11+ | 1, 1, 9 1, 2, 8 1, 3, 7 1, 4, 6 1, 5, 5 2, 2, 7 2, 3, 6 2, 4, 5 3, 3, 5 3, 4, 4 | 10 |
| 12+ | 1, 2, 9 1, 3, 8 1, 4, 7 1, 5, 6 2, 2, 8 2, 3, 7 2, 4, 6 2, 5, 5 3, 3, 6 3, 4, 5 4, 4, 4 | 11 |
| 13+ | 1, 3, 9 1, 4, 8 1, 5, 7 1, 6, 6 2, 2, 9 2, 3, 8 2, 4, 7 2, 5, 6 3, 3, 7 3, 4, 6 3, 5, 5 4, 4, 5 | 12 |
| 14+ | 1, 4, 9 1, 5, 8 1, 6, 7 2, 3, 9 2, 4, 8 2, 5, 7 2, 6, 6 3, 3, 8 3, 4, 7 3, 5, 6 4, 4, 6 4, 5, 5 | 12 |
| 15+ | 1, 5, 9 1, 6, 8 1, 7, 7 2, 4, 9 2, 5, 8 2, 6, 7 3, 3, 9 3, 4, 8 3, 5, 7 3, 6, 6 4, 4, 7 4, 5, 6 5, 5, 5 | 13 |
| 16+ | 1, 6, 9 1, 7, 8 2, 5, 9 2, 6, 8 2, 7, 7 3, 4, 9 3, 5, 8 3, 6, 7 4, 4, 8 4, 5, 7 4, 6, 6 5, 5, 6 | 12 |
| 17+ | 1, 7, 9 1, 8, 8 2, 6, 9 2, 7, 8 3, 5, 9 3, 6, 8 3, 7, 7 4, 4, 9 4, 5, 8 4, 6, 7 5, 5, 7 5, 6, 6 | 12 |
| 18+ | 1, 8, 9 2, 7, 9 2, 8, 8 3, 6, 9 3, 7, 8 4, 5, 9 4, 6, 8 4, 7, 7 5, 5, 8 5, 6, 7 6, 6, 6 | 11 |
| 19+ | 1, 9, 9 2, 8, 9 3, 7, 9 3, 8, 8 4, 6, 9 4, 7, 8 5, 5, 9 5, 6, 8 5, 7, 7 6, 6, 7 | 10 |
| 20+ | 2, 9, 9 3, 8, 9 4, 7, 9 4, 8, 8 5, 6, 9 5, 7, 8 6, 6, 8 6, 7, 7 | 8 |
| 21+ | 3, 9, 9 4, 8, 9 5, 7, 9 5, 8, 8 6, 6, 9 6, 7, 8 7, 7, 7 | 7 |
| 22+ | 4, 9, 9 5, 8, 9 6, 7, 9 6, 8, 8 7, 7, 8 | 5 |
| 23+ | 5, 9, 9 6, 8, 9 7, 7, 9 7, 8, 8 | 4 |
| 24+ | 6, 9, 9 7, 8, 9 8, 8, 8 | 3 |
| 25+ | 7, 9, 9 8, 8, 9 | 2 |
| 26+ | 8, 9, 9 | 1 |
| 27+ | 9, 9, 9 | 1 |
4-Cell Cages
| Target | Possible Combinations | Count |
|---|---|---|
| 4+ | 1, 1, 1, 1 | 1 |
| 5+ | 1, 1, 1, 2 | 1 |
| 6+ | 1, 1, 1, 3 1, 1, 2, 2 | 2 |
| 7+ | 1, 1, 1, 4 1, 1, 2, 3 1, 2, 2, 2 | 3 |
| 8+ | 1, 1, 1, 5 1, 1, 2, 4 1, 1, 3, 3 1, 2, 2, 3 2, 2, 2, 2 | 5 |
| 9+ | 1, 1, 1, 6 1, 1, 2, 5 1, 1, 3, 4 1, 2, 2, 4 1, 2, 3, 3 2, 2, 2, 3 | 6 |
| 10+ | 1, 1, 1, 7 1, 1, 2, 6 1, 1, 3, 5 1, 1, 4, 4 1, 2, 2, 5 1, 2, 3, 4 1, 3, 3, 3 2, 2, 2, 4 2, 2, 3, 3 | 9 |
| 11+ | 1, 1, 1, 8 1, 1, 2, 7 1, 1, 3, 6 1, 1, 4, 5 1, 2, 2, 6 1, 2, 3, 5 1, 2, 4, 4 1, 3, 3, 4 2, 2, 2, 5 2, 2, 3, 4 2, 3, 3, 3 | 11 |
| 12+ | 1, 1, 1, 9 1, 1, 2, 8 1, 1, 3, 7 1, 1, 4, 6 1, 1, 5, 5 1, 2, 2, 7 1, 2, 3, 6 1, 2, 4, 5 1, 3, 3, 5 1, 3, 4, 4 2, 2, 2, 6 2, 2, 3, 5 2, 2, 4, 4 2, 3, 3, 4 3, 3, 3, 3 | 15 |
| 13+ | 1, 1, 2, 9 1, 1, 3, 8 1, 1, 4, 7 1, 1, 5, 6 1, 2, 2, 8 1, 2, 3, 7 1, 2, 4, 6 1, 2, 5, 5 1, 3, 3, 6 1, 3, 4, 5 1, 4, 4, 4 2, 2, 2, 7 2, 2, 3, 6 2, 2, 4, 5 2, 3, 3, 5 2, 3, 4, 4 3, 3, 3, 4 | 17 |
| 14+ | 1, 1, 3, 9 1, 1, 4, 8 1, 1, 5, 7 1, 1, 6, 6 1, 2, 2, 9 1, 2, 3, 8 1, 2, 4, 7 1, 2, 5, 6 1, 3, 3, 7 1, 3, 4, 6 1, 3, 5, 5 1, 4, 4, 5 2, 2, 2, 8 2, 2, 3, 7 2, 2, 4, 6 2, 2, 5, 5 2, 3, 3, 6 2, 3, 4, 5 2, 4, 4, 4 3, 3, 3, 5 3, 3, 4, 4 | 21 |
| 15+ | 1, 1, 4, 9 1, 1, 5, 8 1, 1, 6, 7 1, 2, 3, 9 1, 2, 4, 8 1, 2, 5, 7 1, 2, 6, 6 1, 3, 3, 8 1, 3, 4, 7 1, 3, 5, 6 1, 4, 4, 6 1, 4, 5, 5 2, 2, 2, 9 2, 2, 3, 8 2, 2, 4, 7 2, 2, 5, 6 2, 3, 3, 7 2, 3, 4, 6 2, 3, 5, 5 2, 4, 4, 5 3, 3, 3, 6 3, 3, 4, 5 3, 4, 4, 4 | 23 |
| 16+ | 1, 1, 5, 9 1, 1, 6, 8 1, 1, 7, 7 1, 2, 4, 9 1, 2, 5, 8 1, 2, 6, 7 1, 3, 3, 9 1, 3, 4, 8 1, 3, 5, 7 1, 3, 6, 6 1, 4, 4, 7 1, 4, 5, 6 1, 5, 5, 5 2, 2, 3, 9 2, 2, 4, 8 2, 2, 5, 7 2, 2, 6, 6 2, 3, 3, 8 2, 3, 4, 7 2, 3, 5, 6 2, 4, 4, 6 2, 4, 5, 5 3, 3, 3, 7 3, 3, 4, 6 3, 3, 5, 5 3, 4, 4, 5 4, 4, 4, 4 | 27 |
| 17+ | 1, 1, 6, 9 1, 1, 7, 8 1, 2, 5, 9 1, 2, 6, 8 1, 2, 7, 7 1, 3, 4, 9 1, 3, 5, 8 1, 3, 6, 7 1, 4, 4, 8 1, 4, 5, 7 1, 4, 6, 6 1, 5, 5, 6 2, 2, 4, 9 2, 2, 5, 8 2, 2, 6, 7 2, 3, 3, 9 2, 3, 4, 8 2, 3, 5, 7 2, 3, 6, 6 2, 4, 4, 7 2, 4, 5, 6 2, 5, 5, 5 3, 3, 3, 8 3, 3, 4, 7 3, 3, 5, 6 3, 4, 4, 6 3, 4, 5, 5 4, 4, 4, 5 | 28 |
| 18+ | 1, 1, 7, 9 1, 1, 8, 8 1, 2, 6, 9 1, 2, 7, 8 1, 3, 5, 9 1, 3, 6, 8 1, 3, 7, 7 1, 4, 4, 9 1, 4, 5, 8 1, 4, 6, 7 1, 5, 5, 7 1, 5, 6, 6 2, 2, 5, 9 2, 2, 6, 8 2, 2, 7, 7 2, 3, 4, 9 2, 3, 5, 8 2, 3, 6, 7 2, 4, 4, 8 2, 4, 5, 7 2, 4, 6, 6 2, 5, 5, 6 3, 3, 3, 9 3, 3, 4, 8 3, 3, 5, 7 3, 3, 6, 6 3, 4, 4, 7 3, 4, 5, 6 3, 5, 5, 5 4, 4, 4, 6 4, 4, 5, 5 | 31 |
| 19+ | 1, 1, 8, 9 1, 2, 7, 9 1, 2, 8, 8 1, 3, 6, 9 1, 3, 7, 8 1, 4, 5, 9 1, 4, 6, 8 1, 4, 7, 7 1, 5, 5, 8 1, 5, 6, 7 1, 6, 6, 6 2, 2, 6, 9 2, 2, 7, 8 2, 3, 5, 9 2, 3, 6, 8 2, 3, 7, 7 2, 4, 4, 9 2, 4, 5, 8 2, 4, 6, 7 2, 5, 5, 7 2, 5, 6, 6 3, 3, 4, 9 3, 3, 5, 8 3, 3, 6, 7 3, 4, 4, 8 3, 4, 5, 7 3, 4, 6, 6 3, 5, 5, 6 4, 4, 4, 7 4, 4, 5, 6 4, 5, 5, 5 | 31 |
| 20+ | 1, 1, 9, 9 1, 2, 8, 9 1, 3, 7, 9 1, 3, 8, 8 1, 4, 6, 9 1, 4, 7, 8 1, 5, 5, 9 1, 5, 6, 8 1, 5, 7, 7 1, 6, 6, 7 2, 2, 7, 9 2, 2, 8, 8 2, 3, 6, 9 2, 3, 7, 8 2, 4, 5, 9 2, 4, 6, 8 2, 4, 7, 7 2, 5, 5, 8 2, 5, 6, 7 2, 6, 6, 6 3, 3, 5, 9 3, 3, 6, 8 3, 3, 7, 7 3, 4, 4, 9 3, 4, 5, 8 3, 4, 6, 7 3, 5, 5, 7 3, 5, 6, 6 4, 4, 4, 8 4, 4, 5, 7 4, 4, 6, 6 4, 5, 5, 6 5, 5, 5, 5 | 33 |
| 21+ | 1, 2, 9, 9 1, 3, 8, 9 1, 4, 7, 9 1, 4, 8, 8 1, 5, 6, 9 1, 5, 7, 8 1, 6, 6, 8 1, 6, 7, 7 2, 2, 8, 9 2, 3, 7, 9 2, 3, 8, 8 2, 4, 6, 9 2, 4, 7, 8 2, 5, 5, 9 2, 5, 6, 8 2, 5, 7, 7 2, 6, 6, 7 3, 3, 6, 9 3, 3, 7, 8 3, 4, 5, 9 3, 4, 6, 8 3, 4, 7, 7 3, 5, 5, 8 3, 5, 6, 7 3, 6, 6, 6 4, 4, 4, 9 4, 4, 5, 8 4, 4, 6, 7 4, 5, 5, 7 4, 5, 6, 6 5, 5, 5, 6 | 31 |
| 22+ | 1, 3, 9, 9 1, 4, 8, 9 1, 5, 7, 9 1, 5, 8, 8 1, 6, 6, 9 1, 6, 7, 8 1, 7, 7, 7 2, 2, 9, 9 2, 3, 8, 9 2, 4, 7, 9 2, 4, 8, 8 2, 5, 6, 9 2, 5, 7, 8 2, 6, 6, 8 2, 6, 7, 7 3, 3, 7, 9 3, 3, 8, 8 3, 4, 6, 9 3, 4, 7, 8 3, 5, 5, 9 3, 5, 6, 8 3, 5, 7, 7 3, 6, 6, 7 4, 4, 5, 9 4, 4, 6, 8 4, 4, 7, 7 4, 5, 5, 8 4, 5, 6, 7 4, 6, 6, 6 5, 5, 5, 7 5, 5, 6, 6 | 31 |
| 23+ | 1, 4, 9, 9 1, 5, 8, 9 1, 6, 7, 9 1, 6, 8, 8 1, 7, 7, 8 2, 3, 9, 9 2, 4, 8, 9 2, 5, 7, 9 2, 5, 8, 8 2, 6, 6, 9 2, 6, 7, 8 2, 7, 7, 7 3, 3, 8, 9 3, 4, 7, 9 3, 4, 8, 8 3, 5, 6, 9 3, 5, 7, 8 3, 6, 6, 8 3, 6, 7, 7 4, 4, 6, 9 4, 4, 7, 8 4, 5, 5, 9 4, 5, 6, 8 4, 5, 7, 7 4, 6, 6, 7 5, 5, 5, 8 5, 5, 6, 7 5, 6, 6, 6 | 28 |
| 24+ | 1, 5, 9, 9 1, 6, 8, 9 1, 7, 7, 9 1, 7, 8, 8 2, 4, 9, 9 2, 5, 8, 9 2, 6, 7, 9 2, 6, 8, 8 2, 7, 7, 8 3, 3, 9, 9 3, 4, 8, 9 3, 5, 7, 9 3, 5, 8, 8 3, 6, 6, 9 3, 6, 7, 8 3, 7, 7, 7 4, 4, 7, 9 4, 4, 8, 8 4, 5, 6, 9 4, 5, 7, 8 4, 6, 6, 8 4, 6, 7, 7 5, 5, 5, 9 5, 5, 6, 8 5, 5, 7, 7 5, 6, 6, 7 6, 6, 6, 6 | 27 |
| 25+ | 1, 6, 9, 9 1, 7, 8, 9 1, 8, 8, 8 2, 5, 9, 9 2, 6, 8, 9 2, 7, 7, 9 2, 7, 8, 8 3, 4, 9, 9 3, 5, 8, 9 3, 6, 7, 9 3, 6, 8, 8 3, 7, 7, 8 4, 4, 8, 9 4, 5, 7, 9 4, 5, 8, 8 4, 6, 6, 9 4, 6, 7, 8 4, 7, 7, 7 5, 5, 6, 9 5, 5, 7, 8 5, 6, 6, 8 5, 6, 7, 7 6, 6, 6, 7 | 23 |
| 26+ | 1, 7, 9, 9 1, 8, 8, 9 2, 6, 9, 9 2, 7, 8, 9 2, 8, 8, 8 3, 5, 9, 9 3, 6, 8, 9 3, 7, 7, 9 3, 7, 8, 8 4, 4, 9, 9 4, 5, 8, 9 4, 6, 7, 9 4, 6, 8, 8 4, 7, 7, 8 5, 5, 7, 9 5, 5, 8, 8 5, 6, 6, 9 5, 6, 7, 8 5, 7, 7, 7 6, 6, 6, 8 6, 6, 7, 7 | 21 |
| 27+ | 1, 8, 9, 9 2, 7, 9, 9 2, 8, 8, 9 3, 6, 9, 9 3, 7, 8, 9 3, 8, 8, 8 4, 5, 9, 9 4, 6, 8, 9 4, 7, 7, 9 4, 7, 8, 8 5, 5, 8, 9 5, 6, 7, 9 5, 6, 8, 8 5, 7, 7, 8 6, 6, 6, 9 6, 6, 7, 8 6, 7, 7, 7 | 17 |
| 28+ | 1, 9, 9, 9 2, 8, 9, 9 3, 7, 9, 9 3, 8, 8, 9 4, 6, 9, 9 4, 7, 8, 9 4, 8, 8, 8 5, 5, 9, 9 5, 6, 8, 9 5, 7, 7, 9 5, 7, 8, 8 6, 6, 7, 9 6, 6, 8, 8 6, 7, 7, 8 7, 7, 7, 7 | 15 |
| 29+ | 2, 9, 9, 9 3, 8, 9, 9 4, 7, 9, 9 4, 8, 8, 9 5, 6, 9, 9 5, 7, 8, 9 5, 8, 8, 8 6, 6, 8, 9 6, 7, 7, 9 6, 7, 8, 8 7, 7, 7, 8 | 11 |
| 30+ | 3, 9, 9, 9 4, 8, 9, 9 5, 7, 9, 9 5, 8, 8, 9 6, 6, 9, 9 6, 7, 8, 9 6, 8, 8, 8 7, 7, 7, 9 7, 7, 8, 8 | 9 |
| 31+ | 4, 9, 9, 9 5, 8, 9, 9 6, 7, 9, 9 6, 8, 8, 9 7, 7, 8, 9 7, 8, 8, 8 | 6 |
| 32+ | 5, 9, 9, 9 6, 8, 9, 9 7, 7, 9, 9 7, 8, 8, 9 8, 8, 8, 8 | 5 |
| 33+ | 6, 9, 9, 9 7, 8, 9, 9 8, 8, 8, 9 | 3 |
| 34+ | 7, 9, 9, 9 8, 8, 9, 9 | 2 |
| 35+ | 8, 9, 9, 9 | 1 |
| 36+ | 9, 9, 9, 9 | 1 |
− Subtraction
2-Cell Cages
| Target | Possible Combinations | Count |
|---|---|---|
| 1− | 1, 2 2, 3 3, 4 4, 5 5, 6 6, 7 7, 8 8, 9 | 8 |
| 2− | 1, 3 2, 4 3, 5 4, 6 5, 7 6, 8 7, 9 | 7 |
| 3− | 1, 4 2, 5 3, 6 4, 7 5, 8 6, 9 | 6 |
| 4− | 1, 5 2, 6 3, 7 4, 8 5, 9 | 5 |
| 5− | 1, 6 2, 7 3, 8 4, 9 | 4 |
| 6− | 1, 7 2, 8 3, 9 | 3 |
| 7− | 1, 8 2, 9 | 2 |
| 8− | 1, 9 | 1 |
× Multiplication
2-Cell Cages
| Target | Possible Combinations | Count |
|---|---|---|
| 1× | 1, 1 | 1 |
| 2× | 1, 2 | 1 |
| 3× | 1, 3 | 1 |
| 4× | 1, 4 2, 2 | 2 |
| 5× | 1, 5 | 1 |
| 6× | 1, 6 2, 3 | 2 |
| 7× | 1, 7 | 1 |
| 8× | 1, 8 2, 4 | 2 |
| 9× | 1, 9 3, 3 | 2 |
| 10× | 2, 5 | 1 |
| 12× | 2, 6 3, 4 | 2 |
| 14× | 2, 7 | 1 |
| 15× | 3, 5 | 1 |
| 16× | 2, 8 4, 4 | 2 |
| 18× | 2, 9 3, 6 | 2 |
| 20× | 4, 5 | 1 |
| 21× | 3, 7 | 1 |
| 24× | 3, 8 4, 6 | 2 |
| 25× | 5, 5 | 1 |
| 27× | 3, 9 | 1 |
| 28× | 4, 7 | 1 |
| 30× | 5, 6 | 1 |
| 32× | 4, 8 | 1 |
| 35× | 5, 7 | 1 |
| 36× | 4, 9 6, 6 | 2 |
| 40× | 5, 8 | 1 |
| 42× | 6, 7 | 1 |
| 45× | 5, 9 | 1 |
| 48× | 6, 8 | 1 |
| 49× | 7, 7 | 1 |
| 54× | 6, 9 | 1 |
| 56× | 7, 8 | 1 |
| 63× | 7, 9 | 1 |
| 64× | 8, 8 | 1 |
| 72× | 8, 9 | 1 |
| 81× | 9, 9 | 1 |
3-Cell Cages
| Target | Possible Combinations | Count |
|---|---|---|
| 1× | 1, 1, 1 | 1 |
| 2× | 1, 1, 2 | 1 |
| 3× | 1, 1, 3 | 1 |
| 4× | 1, 1, 4 1, 2, 2 | 2 |
| 5× | 1, 1, 5 | 1 |
| 6× | 1, 1, 6 1, 2, 3 | 2 |
| 7× | 1, 1, 7 | 1 |
| 8× | 1, 1, 8 1, 2, 4 2, 2, 2 | 3 |
| 9× | 1, 1, 9 1, 3, 3 | 2 |
| 10× | 1, 2, 5 | 1 |
| 12× | 1, 2, 6 1, 3, 4 2, 2, 3 | 3 |
| 14× | 1, 2, 7 | 1 |
| 15× | 1, 3, 5 | 1 |
| 16× | 1, 2, 8 1, 4, 4 2, 2, 4 | 3 |
| 18× | 1, 2, 9 1, 3, 6 2, 3, 3 | 3 |
| 20× | 1, 4, 5 2, 2, 5 | 2 |
| 21× | 1, 3, 7 | 1 |
| 24× | 1, 3, 8 1, 4, 6 2, 2, 6 2, 3, 4 | 4 |
| 25× | 1, 5, 5 | 1 |
| 27× | 1, 3, 9 3, 3, 3 | 2 |
| 28× | 1, 4, 7 2, 2, 7 | 2 |
| 30× | 1, 5, 6 2, 3, 5 | 2 |
| 32× | 1, 4, 8 2, 2, 8 2, 4, 4 | 3 |
| 35× | 1, 5, 7 | 1 |
| 36× | 1, 4, 9 1, 6, 6 2, 2, 9 2, 3, 6 3, 3, 4 | 5 |
| 40× | 1, 5, 8 2, 4, 5 | 2 |
| 42× | 1, 6, 7 2, 3, 7 | 2 |
| 45× | 1, 5, 9 3, 3, 5 | 2 |
| 48× | 1, 6, 8 2, 3, 8 2, 4, 6 3, 4, 4 | 4 |
| 49× | 1, 7, 7 | 1 |
| 50× | 2, 5, 5 | 1 |
| 54× | 1, 6, 9 2, 3, 9 3, 3, 6 | 3 |
| 56× | 1, 7, 8 2, 4, 7 | 2 |
| 60× | 2, 5, 6 3, 4, 5 | 2 |
| 63× | 1, 7, 9 3, 3, 7 | 2 |
| 64× | 1, 8, 8 2, 4, 8 4, 4, 4 | 3 |
| 70× | 2, 5, 7 | 1 |
| 72× | 1, 8, 9 2, 4, 9 2, 6, 6 3, 3, 8 3, 4, 6 | 5 |
| 75× | 3, 5, 5 | 1 |
| 80× | 2, 5, 8 4, 4, 5 | 2 |
| 81× | 1, 9, 9 3, 3, 9 | 2 |
| 84× | 2, 6, 7 3, 4, 7 | 2 |
| 90× | 2, 5, 9 3, 5, 6 | 2 |
| 96× | 2, 6, 8 3, 4, 8 4, 4, 6 | 3 |
| 98× | 2, 7, 7 | 1 |
| 100× | 4, 5, 5 | 1 |
| 105× | 3, 5, 7 | 1 |
| 108× | 2, 6, 9 3, 4, 9 3, 6, 6 | 3 |
| 112× | 2, 7, 8 4, 4, 7 | 2 |
| 120× | 3, 5, 8 4, 5, 6 | 2 |
| 125× | 5, 5, 5 | 1 |
| 126× | 2, 7, 9 3, 6, 7 | 2 |
| 128× | 2, 8, 8 4, 4, 8 | 2 |
| 135× | 3, 5, 9 | 1 |
| 140× | 4, 5, 7 | 1 |
| 144× | 2, 8, 9 3, 6, 8 4, 4, 9 4, 6, 6 | 4 |
| 147× | 3, 7, 7 | 1 |
| 150× | 5, 5, 6 | 1 |
| 160× | 4, 5, 8 | 1 |
| 162× | 2, 9, 9 3, 6, 9 | 2 |
| 168× | 3, 7, 8 4, 6, 7 | 2 |
| 175× | 5, 5, 7 | 1 |
| 180× | 4, 5, 9 5, 6, 6 | 2 |
| 189× | 3, 7, 9 | 1 |
| 192× | 3, 8, 8 4, 6, 8 | 2 |
| 196× | 4, 7, 7 | 1 |
| 200× | 5, 5, 8 | 1 |
| 210× | 5, 6, 7 | 1 |
| 216× | 3, 8, 9 4, 6, 9 6, 6, 6 | 3 |
| 224× | 4, 7, 8 | 1 |
| 225× | 5, 5, 9 | 1 |
| 240× | 5, 6, 8 | 1 |
| 243× | 3, 9, 9 | 1 |
| 245× | 5, 7, 7 | 1 |
| 252× | 4, 7, 9 6, 6, 7 | 2 |
| 256× | 4, 8, 8 | 1 |
| 270× | 5, 6, 9 | 1 |
| 280× | 5, 7, 8 | 1 |
| 288× | 4, 8, 9 6, 6, 8 | 2 |
| 294× | 6, 7, 7 | 1 |
| 315× | 5, 7, 9 | 1 |
| 320× | 5, 8, 8 | 1 |
| 324× | 4, 9, 9 6, 6, 9 | 2 |
| 336× | 6, 7, 8 | 1 |
| 343× | 7, 7, 7 | 1 |
| 360× | 5, 8, 9 | 1 |
| 378× | 6, 7, 9 | 1 |
| 384× | 6, 8, 8 | 1 |
| 392× | 7, 7, 8 | 1 |
| 405× | 5, 9, 9 | 1 |
| 432× | 6, 8, 9 | 1 |
| 441× | 7, 7, 9 | 1 |
| 448× | 7, 8, 8 | 1 |
| 486× | 6, 9, 9 | 1 |
| 504× | 7, 8, 9 | 1 |
| 512× | 8, 8, 8 | 1 |
| 567× | 7, 9, 9 | 1 |
| 576× | 8, 8, 9 | 1 |
| 648× | 8, 9, 9 | 1 |
| 729× | 9, 9, 9 | 1 |
4-Cell Cages
| Target | Possible Combinations | Count |
|---|---|---|
| 1× | 1, 1, 1, 1 | 1 |
| 2× | 1, 1, 1, 2 | 1 |
| 3× | 1, 1, 1, 3 | 1 |
| 4× | 1, 1, 1, 4 1, 1, 2, 2 | 2 |
| 5× | 1, 1, 1, 5 | 1 |
| 6× | 1, 1, 1, 6 1, 1, 2, 3 | 2 |
| 7× | 1, 1, 1, 7 | 1 |
| 8× | 1, 1, 1, 8 1, 1, 2, 4 1, 2, 2, 2 | 3 |
| 9× | 1, 1, 1, 9 1, 1, 3, 3 | 2 |
| 10× | 1, 1, 2, 5 | 1 |
| 12× | 1, 1, 2, 6 1, 1, 3, 4 1, 2, 2, 3 | 3 |
| 14× | 1, 1, 2, 7 | 1 |
| 15× | 1, 1, 3, 5 | 1 |
| 16× | 1, 1, 2, 8 1, 1, 4, 4 1, 2, 2, 4 2, 2, 2, 2 | 4 |
| 18× | 1, 1, 2, 9 1, 1, 3, 6 1, 2, 3, 3 | 3 |
| 20× | 1, 1, 4, 5 1, 2, 2, 5 | 2 |
| 21× | 1, 1, 3, 7 | 1 |
| 24× | 1, 1, 3, 8 1, 1, 4, 6 1, 2, 2, 6 1, 2, 3, 4 2, 2, 2, 3 | 5 |
| 25× | 1, 1, 5, 5 | 1 |
| 27× | 1, 1, 3, 9 1, 3, 3, 3 | 2 |
| 28× | 1, 1, 4, 7 1, 2, 2, 7 | 2 |
| 30× | 1, 1, 5, 6 1, 2, 3, 5 | 2 |
| 32× | 1, 1, 4, 8 1, 2, 2, 8 1, 2, 4, 4 2, 2, 2, 4 | 4 |
| 35× | 1, 1, 5, 7 | 1 |
| 36× | 1, 1, 4, 9 1, 1, 6, 6 1, 2, 2, 9 1, 2, 3, 6 1, 3, 3, 4 2, 2, 3, 3 | 6 |
| 40× | 1, 1, 5, 8 1, 2, 4, 5 2, 2, 2, 5 | 3 |
| 42× | 1, 1, 6, 7 1, 2, 3, 7 | 2 |
| 45× | 1, 1, 5, 9 1, 3, 3, 5 | 2 |
| 48× | 1, 1, 6, 8 1, 2, 3, 8 1, 2, 4, 6 1, 3, 4, 4 2, 2, 2, 6 2, 2, 3, 4 | 6 |
| 49× | 1, 1, 7, 7 | 1 |
| 50× | 1, 2, 5, 5 | 1 |
| 54× | 1, 1, 6, 9 1, 2, 3, 9 1, 3, 3, 6 2, 3, 3, 3 | 4 |
| 56× | 1, 1, 7, 8 1, 2, 4, 7 2, 2, 2, 7 | 3 |
| 60× | 1, 2, 5, 6 1, 3, 4, 5 2, 2, 3, 5 | 3 |
| 63× | 1, 1, 7, 9 1, 3, 3, 7 | 2 |
| 64× | 1, 1, 8, 8 1, 2, 4, 8 1, 4, 4, 4 2, 2, 2, 8 2, 2, 4, 4 | 5 |
| 70× | 1, 2, 5, 7 | 1 |
| 72× | 1, 1, 8, 9 1, 2, 4, 9 1, 2, 6, 6 1, 3, 3, 8 1, 3, 4, 6 2, 2, 2, 9 2, 2, 3, 6 2, 3, 3, 4 | 8 |
| 75× | 1, 3, 5, 5 | 1 |
| 80× | 1, 2, 5, 8 1, 4, 4, 5 2, 2, 4, 5 | 3 |
| 81× | 1, 1, 9, 9 1, 3, 3, 9 3, 3, 3, 3 | 3 |
| 84× | 1, 2, 6, 7 1, 3, 4, 7 2, 2, 3, 7 | 3 |
| 90× | 1, 2, 5, 9 1, 3, 5, 6 2, 3, 3, 5 | 3 |
| 96× | 1, 2, 6, 8 1, 3, 4, 8 1, 4, 4, 6 2, 2, 3, 8 2, 2, 4, 6 2, 3, 4, 4 | 6 |
| 98× | 1, 2, 7, 7 | 1 |
| 100× | 1, 4, 5, 5 2, 2, 5, 5 | 2 |
| 105× | 1, 3, 5, 7 | 1 |
| 108× | 1, 2, 6, 9 1, 3, 4, 9 1, 3, 6, 6 2, 2, 3, 9 2, 3, 3, 6 3, 3, 3, 4 | 6 |
| 112× | 1, 2, 7, 8 1, 4, 4, 7 2, 2, 4, 7 | 3 |
| 120× | 1, 3, 5, 8 1, 4, 5, 6 2, 2, 5, 6 2, 3, 4, 5 | 4 |
| 125× | 1, 5, 5, 5 | 1 |
| 126× | 1, 2, 7, 9 1, 3, 6, 7 2, 3, 3, 7 | 3 |
| 128× | 1, 2, 8, 8 1, 4, 4, 8 2, 2, 4, 8 2, 4, 4, 4 | 4 |
| 135× | 1, 3, 5, 9 3, 3, 3, 5 | 2 |
| 140× | 1, 4, 5, 7 2, 2, 5, 7 | 2 |
| 144× | 1, 2, 8, 9 1, 3, 6, 8 1, 4, 4, 9 1, 4, 6, 6 2, 2, 4, 9 2, 2, 6, 6 2, 3, 3, 8 2, 3, 4, 6 3, 3, 4, 4 | 9 |
| 147× | 1, 3, 7, 7 | 1 |
| 150× | 1, 5, 5, 6 2, 3, 5, 5 | 2 |
| 160× | 1, 4, 5, 8 2, 2, 5, 8 2, 4, 4, 5 | 3 |
| 162× | 1, 2, 9, 9 1, 3, 6, 9 2, 3, 3, 9 3, 3, 3, 6 | 4 |
| 168× | 1, 3, 7, 8 1, 4, 6, 7 2, 2, 6, 7 2, 3, 4, 7 | 4 |
| 175× | 1, 5, 5, 7 | 1 |
| 180× | 1, 4, 5, 9 1, 5, 6, 6 2, 2, 5, 9 2, 3, 5, 6 3, 3, 4, 5 | 5 |
| 189× | 1, 3, 7, 9 3, 3, 3, 7 | 2 |
| 192× | 1, 3, 8, 8 1, 4, 6, 8 2, 2, 6, 8 2, 3, 4, 8 2, 4, 4, 6 3, 4, 4, 4 | 6 |
| 196× | 1, 4, 7, 7 2, 2, 7, 7 | 2 |
| 200× | 1, 5, 5, 8 2, 4, 5, 5 | 2 |
| 210× | 1, 5, 6, 7 2, 3, 5, 7 | 2 |
| 216× | 1, 3, 8, 9 1, 4, 6, 9 1, 6, 6, 6 2, 2, 6, 9 2, 3, 4, 9 2, 3, 6, 6 3, 3, 3, 8 3, 3, 4, 6 | 8 |
| 224× | 1, 4, 7, 8 2, 2, 7, 8 2, 4, 4, 7 | 3 |
| 225× | 1, 5, 5, 9 3, 3, 5, 5 | 2 |
| 240× | 1, 5, 6, 8 2, 3, 5, 8 2, 4, 5, 6 3, 4, 4, 5 | 4 |
| 243× | 1, 3, 9, 9 3, 3, 3, 9 | 2 |
| 245× | 1, 5, 7, 7 | 1 |
| 250× | 2, 5, 5, 5 | 1 |
| 252× | 1, 4, 7, 9 1, 6, 6, 7 2, 2, 7, 9 2, 3, 6, 7 3, 3, 4, 7 | 5 |
| 256× | 1, 4, 8, 8 2, 2, 8, 8 2, 4, 4, 8 4, 4, 4, 4 | 4 |
| 270× | 1, 5, 6, 9 2, 3, 5, 9 3, 3, 5, 6 | 3 |
| 280× | 1, 5, 7, 8 2, 4, 5, 7 | 2 |
| 288× | 1, 4, 8, 9 1, 6, 6, 8 2, 2, 8, 9 2, 3, 6, 8 2, 4, 4, 9 2, 4, 6, 6 3, 3, 4, 8 3, 4, 4, 6 | 8 |
| 294× | 1, 6, 7, 7 2, 3, 7, 7 | 2 |
| 300× | 2, 5, 5, 6 3, 4, 5, 5 | 2 |
| 315× | 1, 5, 7, 9 3, 3, 5, 7 | 2 |
| 320× | 1, 5, 8, 8 2, 4, 5, 8 4, 4, 4, 5 | 3 |
| 324× | 1, 4, 9, 9 1, 6, 6, 9 2, 2, 9, 9 2, 3, 6, 9 3, 3, 4, 9 3, 3, 6, 6 | 6 |
| 336× | 1, 6, 7, 8 2, 3, 7, 8 2, 4, 6, 7 3, 4, 4, 7 | 4 |
| 343× | 1, 7, 7, 7 | 1 |
| 350× | 2, 5, 5, 7 | 1 |
| 360× | 1, 5, 8, 9 2, 4, 5, 9 2, 5, 6, 6 3, 3, 5, 8 3, 4, 5, 6 | 5 |
| 375× | 3, 5, 5, 5 | 1 |
| 378× | 1, 6, 7, 9 2, 3, 7, 9 3, 3, 6, 7 | 3 |
| 384× | 1, 6, 8, 8 2, 3, 8, 8 2, 4, 6, 8 3, 4, 4, 8 4, 4, 4, 6 | 5 |
| 392× | 1, 7, 7, 8 2, 4, 7, 7 | 2 |
| 400× | 2, 5, 5, 8 4, 4, 5, 5 | 2 |
| 405× | 1, 5, 9, 9 3, 3, 5, 9 | 2 |
| 420× | 2, 5, 6, 7 3, 4, 5, 7 | 2 |
| 432× | 1, 6, 8, 9 2, 3, 8, 9 2, 4, 6, 9 2, 6, 6, 6 3, 3, 6, 8 3, 4, 4, 9 3, 4, 6, 6 | 7 |
| 441× | 1, 7, 7, 9 3, 3, 7, 7 | 2 |
| 448× | 1, 7, 8, 8 2, 4, 7, 8 4, 4, 4, 7 | 3 |
| 450× | 2, 5, 5, 9 3, 5, 5, 6 | 2 |
| 480× | 2, 5, 6, 8 3, 4, 5, 8 4, 4, 5, 6 | 3 |
| 486× | 1, 6, 9, 9 2, 3, 9, 9 3, 3, 6, 9 | 3 |
| 490× | 2, 5, 7, 7 | 1 |
| 500× | 4, 5, 5, 5 | 1 |
| 504× | 1, 7, 8, 9 2, 4, 7, 9 2, 6, 6, 7 3, 3, 7, 8 3, 4, 6, 7 | 5 |
| 512× | 1, 8, 8, 8 2, 4, 8, 8 4, 4, 4, 8 | 3 |
| 525× | 3, 5, 5, 7 | 1 |
| 540× | 2, 5, 6, 9 3, 4, 5, 9 3, 5, 6, 6 | 3 |
| 560× | 2, 5, 7, 8 4, 4, 5, 7 | 2 |
| 567× | 1, 7, 9, 9 3, 3, 7, 9 | 2 |
| 576× | 1, 8, 8, 9 2, 4, 8, 9 2, 6, 6, 8 3, 3, 8, 8 3, 4, 6, 8 4, 4, 4, 9 4, 4, 6, 6 | 7 |
| 588× | 2, 6, 7, 7 3, 4, 7, 7 | 2 |
| 600× | 3, 5, 5, 8 4, 5, 5, 6 | 2 |
| 625× | 5, 5, 5, 5 | 1 |
| 630× | 2, 5, 7, 9 3, 5, 6, 7 | 2 |
| 640× | 2, 5, 8, 8 4, 4, 5, 8 | 2 |
| 648× | 1, 8, 9, 9 2, 4, 9, 9 2, 6, 6, 9 3, 3, 8, 9 3, 4, 6, 9 3, 6, 6, 6 | 6 |
| 672× | 2, 6, 7, 8 3, 4, 7, 8 4, 4, 6, 7 | 3 |
| 675× | 3, 5, 5, 9 | 1 |
| 686× | 2, 7, 7, 7 | 1 |
| 700× | 4, 5, 5, 7 | 1 |
| 720× | 2, 5, 8, 9 3, 5, 6, 8 4, 4, 5, 9 4, 5, 6, 6 | 4 |
| 729× | 1, 9, 9, 9 3, 3, 9, 9 | 2 |
| 735× | 3, 5, 7, 7 | 1 |
| 750× | 5, 5, 5, 6 | 1 |
| 756× | 2, 6, 7, 9 3, 4, 7, 9 3, 6, 6, 7 | 3 |
| 768× | 2, 6, 8, 8 3, 4, 8, 8 4, 4, 6, 8 | 3 |
| 784× | 2, 7, 7, 8 4, 4, 7, 7 | 2 |
| 800× | 4, 5, 5, 8 | 1 |
| 810× | 2, 5, 9, 9 3, 5, 6, 9 | 2 |
| 840× | 3, 5, 7, 8 4, 5, 6, 7 | 2 |
| 864× | 2, 6, 8, 9 3, 4, 8, 9 3, 6, 6, 8 4, 4, 6, 9 4, 6, 6, 6 | 5 |
| 875× | 5, 5, 5, 7 | 1 |
| 882× | 2, 7, 7, 9 3, 6, 7, 7 | 2 |
| 896× | 2, 7, 8, 8 4, 4, 7, 8 | 2 |
| 900× | 4, 5, 5, 9 5, 5, 6, 6 | 2 |
| 945× | 3, 5, 7, 9 | 1 |
| 960× | 3, 5, 8, 8 4, 5, 6, 8 | 2 |
| 972× | 2, 6, 9, 9 3, 4, 9, 9 3, 6, 6, 9 | 3 |
| 980× | 4, 5, 7, 7 | 1 |
| 1000× | 5, 5, 5, 8 | 1 |
| 1008× | 2, 7, 8, 9 3, 6, 7, 8 4, 4, 7, 9 4, 6, 6, 7 | 4 |
| 1024× | 2, 8, 8, 8 4, 4, 8, 8 | 2 |
| 1029× | 3, 7, 7, 7 | 1 |
| 1050× | 5, 5, 6, 7 | 1 |
| 1080× | 3, 5, 8, 9 4, 5, 6, 9 5, 6, 6, 6 | 3 |
| 1120× | 4, 5, 7, 8 | 1 |
| 1125× | 5, 5, 5, 9 | 1 |
| 1134× | 2, 7, 9, 9 3, 6, 7, 9 | 2 |
| 1152× | 2, 8, 8, 9 3, 6, 8, 8 4, 4, 8, 9 4, 6, 6, 8 | 4 |
| 1176× | 3, 7, 7, 8 4, 6, 7, 7 | 2 |
| 1200× | 5, 5, 6, 8 | 1 |
| 1215× | 3, 5, 9, 9 | 1 |
| 1225× | 5, 5, 7, 7 | 1 |
| 1260× | 4, 5, 7, 9 5, 6, 6, 7 | 2 |
| 1280× | 4, 5, 8, 8 | 1 |
| 1296× | 2, 8, 9, 9 3, 6, 8, 9 4, 4, 9, 9 4, 6, 6, 9 6, 6, 6, 6 | 5 |
| 1323× | 3, 7, 7, 9 | 1 |
| 1344× | 3, 7, 8, 8 4, 6, 7, 8 | 2 |
| 1350× | 5, 5, 6, 9 | 1 |
| 1372× | 4, 7, 7, 7 | 1 |
| 1400× | 5, 5, 7, 8 | 1 |
| 1440× | 4, 5, 8, 9 5, 6, 6, 8 | 2 |
| 1458× | 2, 9, 9, 9 3, 6, 9, 9 | 2 |
| 1470× | 5, 6, 7, 7 | 1 |
| 1512× | 3, 7, 8, 9 4, 6, 7, 9 6, 6, 6, 7 | 3 |
| 1536× | 3, 8, 8, 8 4, 6, 8, 8 | 2 |
| 1568× | 4, 7, 7, 8 | 1 |
| 1575× | 5, 5, 7, 9 | 1 |
| 1600× | 5, 5, 8, 8 | 1 |
| 1620× | 4, 5, 9, 9 5, 6, 6, 9 | 2 |
| 1680× | 5, 6, 7, 8 | 1 |
| 1701× | 3, 7, 9, 9 | 1 |
| 1715× | 5, 7, 7, 7 | 1 |
| 1728× | 3, 8, 8, 9 4, 6, 8, 9 6, 6, 6, 8 | 3 |
| 1764× | 4, 7, 7, 9 6, 6, 7, 7 | 2 |
| 1792× | 4, 7, 8, 8 | 1 |
| 1800× | 5, 5, 8, 9 | 1 |
| 1890× | 5, 6, 7, 9 | 1 |
| 1920× | 5, 6, 8, 8 | 1 |
| 1944× | 3, 8, 9, 9 4, 6, 9, 9 6, 6, 6, 9 | 3 |
| 1960× | 5, 7, 7, 8 | 1 |
| 2016× | 4, 7, 8, 9 6, 6, 7, 8 | 2 |
| 2025× | 5, 5, 9, 9 | 1 |
| 2048× | 4, 8, 8, 8 | 1 |
| 2058× | 6, 7, 7, 7 | 1 |
| 2160× | 5, 6, 8, 9 | 1 |
| 2187× | 3, 9, 9, 9 | 1 |
| 2205× | 5, 7, 7, 9 | 1 |
| 2240× | 5, 7, 8, 8 | 1 |
| 2268× | 4, 7, 9, 9 6, 6, 7, 9 | 2 |
| 2304× | 4, 8, 8, 9 6, 6, 8, 8 | 2 |
| 2352× | 6, 7, 7, 8 | 1 |
| 2401× | 7, 7, 7, 7 | 1 |
| 2430× | 5, 6, 9, 9 | 1 |
| 2520× | 5, 7, 8, 9 | 1 |
| 2560× | 5, 8, 8, 8 | 1 |
| 2592× | 4, 8, 9, 9 6, 6, 8, 9 | 2 |
| 2646× | 6, 7, 7, 9 | 1 |
| 2688× | 6, 7, 8, 8 | 1 |
| 2744× | 7, 7, 7, 8 | 1 |
| 2835× | 5, 7, 9, 9 | 1 |
| 2880× | 5, 8, 8, 9 | 1 |
| 2916× | 4, 9, 9, 9 6, 6, 9, 9 | 2 |
| 3024× | 6, 7, 8, 9 | 1 |
| 3072× | 6, 8, 8, 8 | 1 |
| 3087× | 7, 7, 7, 9 | 1 |
| 3136× | 7, 7, 8, 8 | 1 |
| 3240× | 5, 8, 9, 9 | 1 |
| 3402× | 6, 7, 9, 9 | 1 |
| 3456× | 6, 8, 8, 9 | 1 |
| 3528× | 7, 7, 8, 9 | 1 |
| 3584× | 7, 8, 8, 8 | 1 |
| 3645× | 5, 9, 9, 9 | 1 |
| 3888× | 6, 8, 9, 9 | 1 |
| 3969× | 7, 7, 9, 9 | 1 |
| 4032× | 7, 8, 8, 9 | 1 |
| 4096× | 8, 8, 8, 8 | 1 |
| 4374× | 6, 9, 9, 9 | 1 |
| 4536× | 7, 8, 9, 9 | 1 |
| 4608× | 8, 8, 8, 9 | 1 |
| 5103× | 7, 9, 9, 9 | 1 |
| 5184× | 8, 8, 9, 9 | 1 |
| 5832× | 8, 9, 9, 9 | 1 |
| 6561× | 9, 9, 9, 9 | 1 |
÷ Division
2-Cell Cages
| Target | Possible Combinations | Count |
|---|---|---|
| 2÷ | 1, 2 2, 4 3, 6 4, 8 | 4 |
| 3÷ | 1, 3 2, 6 3, 9 | 3 |
| 4÷ | 1, 4 2, 8 | 2 |
| 5÷ | 1, 5 | 1 |
| 6÷ | 1, 6 | 1 |
| 7÷ | 1, 7 | 1 |
| 8÷ | 1, 8 | 1 |
| 9÷ | 1, 9 | 1 |